Duality of tensor products of converge-free spaces.
Let E and F be two vector spaces in separating duality. Let us consider T0, the uniform convergence topology on E on the partial sums of families of F which are weakly summable to 0 in F; then, if (E',T'0) is the completion of (E,T0), the finest locally convex topology T on F for which all the weakly summable families in F are also T-summable, is the uniform convergence topology on the T'0-compact subsets of E'. If F is a Banach space and E its dual space F', every weakly summable family in F is...
On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space is equal to , and therefore that its dual is BMO. We also prove the atomic decomposition for for p ≤ 1 close enough to 1.